In this study, children and adolescents will be evaluated for the presence of both ADHD and Anxiety Disorder. Approximately 120 children and adolescents with both disorders who meet all the study entry requirements (such as being otherwise medically healthy) will be enrolled. Children and adolescents who are not on a stable dose of a stimulant will first be treated openly with methylphenidate for 6 weeks. Those whose ADHD does not improve during this initial treatment period will not continue in the study but will be referred for further support in the community. Those who show improvement in both their ADHD and anxiety symptoms will stay on methylphenidate for an additional 8 weeks. Those who show improvement in ADHD but not anxiety will be asked to enter the double-blind phase of the study. In this phase, participants will be randomized (assigned by chance) to receive either fluvoxamine or placebo, in combination with stimulant/methylphenidate, for 8 weeks. Children or adolescents who enter the study on a stable dose of stimulant will move directly to the Double-Blind phase. Participants who are assigned to placebo and who do not show an improvement in anxiety after 8 weeks will be eligible for an additional 8 weeks of open treatment with the methylphenidate/stimulant and fluvoxamine combination. At the end of the trial, clinical care will be provided for up to an additional month until referral to an outside clinician can be arranged.